Question
Find Greatest Common Divisor of 240 and 180, using repeated division.
Answer
The GCD of given numbers is 12.
Explanation
Step 1 : Place the numbers inside division bar:.
| 240 | 180 |
Step 2 : Divide numbers by 2.
| 2 | 240 | 180 |
| 120 | 90 |
Step 3 : Divide numbers by 2.
| 2 | 240 | 180 |
| 2 | 120 | 90 |
| 60 | 45 |
Step 4 : Divide numbers by 3.
| 2 | 240 | 180 |
| 2 | 120 | 90 |
| 3 | 60 | 45 |
| 20 | 15 |
Step 5 : Number 20 and 15, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3 = 12 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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